The present invention relates generally to magnetic resonance (MR) imaging, and more specifically, to a system and method which provide for B1 amplitude reduction in RF pulse design. By adjusting peak or high amplitude portions of an RF pulse and the corresponding gradient waveforms, overall RF transmit power can be reduced, and the specific absorption rate (SAR) of the pulse can be controlled. Such a reduction in amplitude can be extended for non-linear k-space trajectories, such as for spiral and non-uniform trajectories.
MR imaging in general is based upon the principle of nuclear magnetic resonance. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field, such as a B1 excitation field, which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized, encoded, and processed to acquire a set of data known as k-space data. This data is then used to reconstruct an image using one of many well known reconstruction techniques. The shape of the magnetic field gradient waveforms contributes to the manner and order in which the k-space data is acquired, also known as a k-space trajectory.
During a transmit sequence, an MR system will also transmit RF pulses having specially designed frequencies and amplitude profiles while the magnetic field gradients are being applied. For example, an MR system might transmit an excitation pulse at a particular frequency and amplitude for a particular time, in order to induce a net transverse magnetization in nuclei of a scan subject. Subsequent pulses transmitted by the system may have the same or a similar frequency, but might have different gain, amplitude, or duration attributes to cause a different change in magnetization (or “flip angle”). In addition, the attributes of RF pulses can be adjusted such that only spins within a given 2D or 3D portion of a scan subject are affected. This is useful in such techniques as reduced field of view imaging or spatially-selective imaging. Thus, in general, the particular shapes of the RF pulses in a transmit sequence are varied to manipulate the net magnetization in nuclei of scan subject.
Presently, RF pulses are designed using a variety of techniques, via both direct and approximation approaches. A few exemplary design techniques include the Shinnar-LeRoux technique, the small tip angle (STA) approximation, the linear class large tip angle (LCLTA) approximation, techniques based upon EPI trajectories, and other determinations based upon the Bloch equations. It is often the case, however, that these RF pulse design techniques produce RF pulses having profiles with one or more segments of undesirably high amplitudes. For example, a complex RF pulse shape associated with a 2D or 3D spatially-selective RF pulse can sometimes have a peak amplitude segment that exceeds desired SAR limits. Additionally, such an RF pulse might have high amplitude portions which result in an RF transmission power exceeding the maximum achievable transmission power of a given system. A peak amplitude segment may often be associated with the portion of the pulse corresponding to near the origin of the excitation k-space. Therefore, it has been appreciated that accommodation should be made to improve the transmission characteristics of these portions of RF pulses.
One way to reduce peak RF amplitude and SAR is to reduce the amplitude of the entire RF pulse and proportionately lengthen the pulse, while performing the same operation to the gradient waveforms, thereby producing the same magnetization or flip angle profiles. For example, the amplitude of an RF pulse could be quartered, and the duration quadrupled. However, such an approach may be deemed impracticable in many circumstances, since the result could be an RF pulse with a rather long duration. Longer durations of RF pulses can cause reduced image quality due to relaxation, off-resonance frequency, etc.
Another type of pulse modification which may limit high amplitude or high transmit power portions of an RF pulse design is known as the variable rate selective excitation (VERSE) technique. Implementations of the VERSE technique “time-dilate” the local shape of RF pulses and gradient waveforms to reduce peak B1 amplitude while satisfying such hardware constraints as maximum gradient amplitude and slew-rate. By using the time-dilation function, the VERSE technique provides more practical control over peak B1 amplitude and SAR, as compared to conventionally designed pulses or stretched pulses. That is, VERSE pulses are typically employed as a technique for reducing peak power over a high amplitude portion of a pulse. However, to date, the VERSE technique has been known to be implementable only for common, single dimensional (1D) spatially-selective RF pulses with constant gradients.
Generally, VERSE pulses are RF pulses which have been derived from a pre-existing, conventionally designed RF pulse. The conventionally designed RF pulse can be produced by any of a variety of design methods for a desired flip angle, duration, bandwidth, etc. Where a portion of the RF pulse is undesirably high in amplitude, the VERSE technique can be applied in a post-design processing to proportionately reduce and lengthen only the undesirably high portion of the RF pulse. In turn, the corresponding portion of the slice-select gradient waveform is similarly reduced and lengthened, to maintain the desired slice selection.
As shown in FIG. 1, an exemplary constant magnitude slice-select gradient waveform 100 may, in implementation, take the general form of a trapezoid for transmission with an exemplary 1D RF pulse. The associated RF pulse 102 may generally be a sinc pulse. The gradient waveform is designed having a first ramp 112 increasing to a constant amplitude segment 110, then followed by a decreasing ramp 114. The RF pulse 102 has a first sidelobe 106, a mainlobe 104 having a higher amplitude, and a second side lobe 108. According to the VERSE technique, pulse 102 and waveform 100 may be adjusted to control SAR during the mainlobe 104 of the RF pulse 100.
Generally, to reduce peak RF amplitude and control SAR using the VERSE technique, the high amplitude segment 104 of the RF pulse can be reshaped, after the pulse 102 was initially designed. Thus, a VERSE RF pulse 118 is generally characterized by a lengthened or stretched mainlobe segment 120, while the sidelobes 122, 124 remain relatively unchanged. Thus, the peak RF amplitude is reduced, and the RF power from the peak segment 104 of the conventionally designed pulse 102 is spread over a longer segment 120 in the VERSE pulse 118. The stretched segment 118 of the VERSE RF pulse 118 is then transmitted in the presence of a lengthened, reduced slice select (Gz) gradient 116, to maintain the net desired flip angle, while controlling the effective B1 field and SAR. Thus, the center portion 132 of the gradient waveform corresponding in time to the stretched mainlobe 120 has been reduced and stretched. The remaining portions 128 and 136 of the constant amplitude section of the gradient pulse 116, as well as the ramps 126 and 138 remain the same. Thus, the VERSE technique provides a post-design way to control SAR without lengthening the duration of an entire pulse.
However, the VERSE technique is not presently known to be directly applicable for sequences that use spiral or other non-linear or non-uniform k-space trajectories, such as those used with two dimensional (2D) spatially-selective RF pulses. One challenge in applying VERSE to non-Cartesian k-space trajectories (e.g., a spiral) is that the time dilation function and its derivatives get propagated, via the chain rule of differentiation, into the gradient and slew-rate expressions. Therefore enforcing gradient amplitude constraints and slew-rate constraints would lead to complicated differential inequalities, which would be difficult to solve.
Another challenge in directly applying VERSE to non-Cartesian trajectories is the limitations on waveform shapes imposed by hardware constraints. To illustrate, FIG. 2 depicts an exemplary frequency encoding (Gx) gradient waveform 140 to implement a non-Cartesian, spiral k-space trajectory. If the VERSE technique, as described above, was directly applied to waveform 140, the portion 144 corresponding to a high amplitude RF segment would be stretched in duration and decreased in amplitude, while the remainder 148 of the pulse would be unchanged. However, as shown, such a technique would create a sharp change or discontinuity 146 in the waveform where the two segments 144, 148 meet. Such a discontinuity 146 is not known to be implementable by gradient coil assemblies, due to slew rate constraints. As such, the advantages of a VERSE-type SAR reduction have not been used for non-uniform or non-Cartesian k-space trajectories.
It would therefore be desirable to have a system and method capable of reducing B1 power during a portion of an RF pulse designed according to a non-Cartesian k-space trajectory. It would be further desirable for embodiments of such a system and method to quickly and efficiently calculate adjustments to existing RF pulse profiles and gradient waveforms and to maintain a relatively short transmit duration of the pulses.